Question

Eighteen pairs of measurements were taken at random to estimate the relationship between variables X and Y. A least-squares line was fitted to the collected data. The resulting residual plot is shown. A residual plot is shown with 18 points scattered above and below the x-axis in such a way that the distance from the x-axis increases as you move from left to right. Which of the following conclusions is appropriate?

Answer 1

Step-by-step explanation:

Without specific information about the given options for conclusions, it is not possible to determine which one is appropriate based solely on the description provided.

However, based on the given description of the residual plot, where the points are scattered above and below the x-axis in a pattern where the distance from the x-axis increases as you move from left to right, it suggests that the least-squares line may not be the best fit for the data. The pattern of the residuals indicates that the relationship between variables X and Y might not be linear, and a different type of model or curve could potentially provide a better fit.

Therefore, a possible appropriate conclusion could be that the linear regression model may not adequately capture the relationship between variables X and Y, and further analysis is required to explore alternative models or relationships between the variables.

Answer 2

The appropriate conclusion is that there is a significant linear relationship between X and Y, and the regression line can be used to model this relationship in the population.

Step-by-step explanation:

In this case, the fact that the residuals are scattered both above and below the x-axis and the distance from the x-axis increases as you move from left to right suggests a linear relationship between the variables X and Y. The least-squares line fitted to the data indicates the best-fit line that minimizes the sum of squared errors and represents the linear relationship between the two variables. Therefore, the appropriate conclusion is that there is a significant linear relationship between X and Y, and the regression line can be used to model this relationship in the population.